5-8 mile hike to a good lake campsite in GNP?

Gunsight Lake, Lake Elizabeth, Coosely Lake. There many more but be aware that Glacier is not particularly known for it's fishing. This may help:
www.amazon.com/Fishing-Glacier-National-Park/dp/0762710993/ref=sr_1_1?s=books&ie=UTF8&qid=1480642752&sr=1-1&keywords=fishing+glacier+national+pa

From the Two Medicine Lake area, heading in to Old Man Lake (about 6 miles) and camping there might be a good option. Supposed to have decent fishing. You could camp both nights there, or hike about 8 miles over to No Name Lake and camp the next night there. Not sure if No Name Lake has fish or not, but I don't think it does. Really pretty lake, though.

If you do the loop it is the Dawson Pass to Pitamakin Pass Loop and it is around 16-18 miles total, with the option of taking a small tourist boat to/from the starting point if you time things right. So that's pretty neat, the view from the boat when it is on Two Medicine Lake is pretty breathtaking.

Really gorgeous hike, especially along the ridge between Dawson Pass and Pitamakin Pass.

I would just go along with what Mark and Hikerjer already mentioned. Personally, I haven't gotten into fishing yet, at least not in Glacier, so I really can't speak from experience. I have heard that Old Man Lake use to be great fishing, but with the heavy backcountry use Glacier gets, I don't know how true that is anymore. I've seen several fish pulled out of the middle and north fork of the Flathead River, but there isn't much backcountry camping you can do along those.

I have been told numerous stories about some of the deeper, off trail backcountry lakes. Cerulean Lake is one that is constantly recurring. Someone that trapped Wolverines in the park for years told me that it is the best fishing hole in Glacier. But there is no easy way to get there. You would have to hike in to Quartz Lake, use a packraft for several miles to cross the lake, and then bush whack through a lot of bad stuff for a few more miles to get there.

Perhaps Kintla, Bowman, Quartz, and Logging Lake offer some good fishing. I'm kind of surprised nothing is coming to mind of those. Grace Lake doesn't get all that much use, so it might be a good spot. There are 2 lakes above Grace Lake that rarely get seen. There is an old trail that goes up that way, although lots of downfall covers it (NO Matter what, follow that trail). A base camp at Grace Lake though would give you a whole day to explore all 3 of those lakes, plus fishing at Logging Lake on the way in and out.

The Camas Lake drainage is a good one. Trout Lake, Arrow Lake, Camas Lake, Lake Evangeline, and Ruger Lake. You could camp at Arrow or Camas, and fish the others. There is even another lake below those, although I don't remember the name. That was great fishing in the past, but I can't speak on it nowadays. Dutch Lake might be another great option. No one goes up there. The trail is brushy, but pretty easy to follow. The park service will grant you undesignated camping up there. With no one ever going up there, I imagine the fishing has to be good.

Another lake I've heard has good fishing is Lake Isabel, which is a pretty lake. Part of the area is burnt forest, but it's still a beautiful area, and has a few small lakes around it that may offer some better fishing.

Perhaps others can chime in with there experiences. Also, maybe check some of the Glacier Facebook pages, or even email the park backcountry office. There is a Glacier Park forum as well, which might offer some more insight on the fishing.